Analysis of one-dimensional stochastic finite elements using neural networks

This paper explores the applicability of neural networks for analyzing the uncertainty spread of structural responses under the presence of one-dimensional random fields. Specifically, the neural network is intended to be a partial surrogate of the structural model needed in a Monte Carlo simulation, due to its associative memory properties. The network is trained with some pairs of input and output data obtained by some Monte Carlo simulations and then used in substitution of the finite element solver. In order to minimize the size of the networks, and hence the number of training pairs, the Karhunen–Loéve decomposition is applied as an optimal feature extraction tool. The Monte Carlo samples for training and validation are also generated using this decomposition. The Nyström technique is employed for the numerical solution of the Fredholm integral equation. The radial basis function (RBF) network was selected as the neural device for learning the input/output relationship due to its high accuracy and fast training speed. The analysis shows that this approach constitutes a promising method for stochastic finite element analysis inasmuch as the error with respect to the Monte Carlo simulation is negligible.     

Heat‐flux‐specified boundary treatment for gas flow and heat transfer in microchannel using direct simulation Monte Carlo method

Direct simulation Monte Carlo (DSMC) method has been widely used to study gaseous flow and heat transfer in micro‐fluidic devices. For flows associated with microelectromechanical systems (MEMS), the heat‐flux‐specified (HFS) boundary condition broadly exists. However, problems with HFS boundary have not been realized in the simulation of microchannel flows with DSMC method. To overcome this problem, a new technique named as inverse temperature sampling (ITS) is developed. This technique provides an approach to calculate the molecular reflective characteristic temperature from the specified heat flux at the wall boundary. Coupling with DSMC method, the ITS technique can treat the HFS boundary condition in DSMC method for both simple gas and gas mixtures. For validation, heat flux obtained from two‐dimensional Poiseuille flows with wall‐temperature‐specified (WTS) boundary condition is employed as the initial thermal boundary condition of our new method. Sampled wall temperature by the ITS method agrees well with the expected value. Pressure, velocity and temperature distributions under these two thermal boundary conditions (WTS and HFS) are compared. Effects of molecule collision model and gas–surface interaction model are also investigated. Results show that the proposed ITS method could accurately simulate gaseous flow and heat transfer in MEMS. Copyright © 2007 John Wiley & Sons, Ltd.     

Asymptotic modelling of flows in microchannel by using Navier-Stokes or Burnett equations and comparison with DSMC simulations

The modelling of isothermal gas flows driven by pressure drops, in coplanar microchannels is investigated. The goal is to construct an asymptotic model deduced from Navier-Stokes or Burnett equations for this type of flow, assuming slip boundary conditions along the walls. The dimensionless balance equations are written, taking into account a geometrical parameter introduced in this study. The application of the Principle of Least Degeneracy produces models with small Mach numbers and small or moderate Knudsen numbers and allows the development of asymptotic models. The first and second approximations associated with the Navier-Stokes or Burnett equations are presented and discussed. Navier-Stokes and Burnett second approximations reduce the mass flow rates.Additionally, first asymptotic solutions as against Direct Simulation Monte Carlo (DSMC) simulations show overall satisfactory agreements.     

空气焓值法测量全年能源消耗效率不确定度评定方法研究

以焓值法的直接测试量表征的制冷量和制热量计算公式作为基础数学模型,采用GUM法和蒙特卡洛法相结合的方法来评定全年能源消耗效率(APF)的不确定度。由于焓值法数学模型呈现出明显的非线性,首先使用蒙特卡洛法来验证额定制冷量和额定制热量GUM法评定结果, 验证结果显示2种方法偏差不超过2‰。然后,给出了5个工况下换热量的不确定度评定结果,以此作为APF蒙特卡洛模拟的输入量,并给出了自适应蒙特卡洛法评定APF不确定度模拟流程,得到某空调的APF扩展不确定度评定结果为0.09 kW·h/(kW·h)（k=2）。     

手持式激光测距仪"测距标准偏差综合评定"的扩展不确定度

在确定的函数关系(数学模型)中,因变量(输出量)随自变量(输入量)的变化规律完全由数学逻辑所确定,自变量到因变量的传递系数(灵敏系数)也可由因变量的标准差和自变量的标准差之比所决定,而与自变量的来历(测量的或者给定的)没有关系[1].本文根据这一基本原理,采用模拟自变量随机变化的方法,成功计算了手持式激光测距仪的测距固定偏差和比例偏差系数的测量不确定度,从而计算出测距标准差综合评定的扩展不确定度,同时解决了复杂的数学模型中多个输入量到输出量的灵敏系数和输出量的不确定度的计算问题.     

基于自适应蒙特卡罗方法的测量不确定度评定

在GUM Sup.1提出基于分布传播的不确定度评定基础上,系统地介绍了自适应蒙特卡罗方法进行不确定度评定的原理和步骤,并以此对线性测量模型和非线性测量模型进行了仿真,得出自适应蒙特卡罗方法对两类测量模型不确定度都有较好的评定效果,同时指出自适应蒙特卡罗方法中仿真次数M和数值容差δ的合理选择都需要进一步研究。     

Uncertainty propagation for deterministic models of biochemical networks using moment equations and the extended Kalman filter

Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.     

A comparison of techniques for evaluating hydrologic model uncertainty

Hydrologic models are composed of several components which are all parameter dependent. In the general setting, parameter values are selected based on regionalization of observed rainfall-runoff events, or upon calibration at local stream gauge data when available. Based on these data, a selected parameter set is then used for the hydrologic model. However, seldom are hydrologic model outputs examined as to the total variations in output due to the independent but coupled variations in parameter input values. In this paper, three of the more common techniques for evaluating model output distributions are compared as applied to a selected hydrologic model; i.e., an exhaustion techniques, Monte Carlo simulation method, and the more recently advanced Rosenblueth technique. It is concluded that, for the hydrologic model considered, the Monte Carlo technique provides more accuracy in comparison to Rosenblueth technique (for the same computational effort), but is less accurate than Exhaustion.     

Reliability Analysis of Slope Stability Considering Temporal Variations of Rock Mass Properties

Temporal variation of rock mass properties, especially the strength degradation due to drying-wetting cycles as well as the acidic wetting fluid (rainfall or reservoir water) is crucial to stability of reservoir rock slopes. Based on a series of drying-wetting cycling and experiments considering the influences of pH values, the degradation degree models of the reduced cohesion c′, friction angle φ′ are developed. 2D stability analysis of the slope is subsequently carried out to calculate the factor of safety (Fs) via limit equilibrium method (LEM) and a predictive model of Fs is built using multivariate adaptive regression splines (MARS), revealing the effect of the dryingwetting cycles and pH value. The reliability analysis by Monte Carlo simulation is performed to rationally consider the uncertainty and the temporal variation of the shear strength parameters of rock mass. Results indicate that the MARS-based model can estimate the Fs accurately. The Fs and the reliability index β decrease with increase of drying-wetting cycles, and the temporal variation of rock mass properties has significant influence on the slope reliability. Overlooking the temporal variation of rock properties may overestimate the Fs and reliability index β in the longer term.     

基于形状误差不确定度的大尺寸测量系统优化配置方法

针对大尺寸测量系统部署问题,提出了面向测量任务的以形状误差不确定度为评价指标的优化配置测量系统的方法。对于基于蒙特卡罗仿真方法的测量点仿真和多测量仪器数据融合进行了研究。在建立形状误差评定模型基础上,提出并实现了基于粒子群算法的形状误差评定模型的求解及基于蒙特卡罗法的形状误差不确定度计算方法。通过某卫星舱段端框的仿真试验,验证了以不确定度为指标进行大尺寸测量系统配置方法的有效性,可为大尺寸测量系统现场快速部署提供方案指导。     

THE AGGLOMERATION AND AGING OF TEREPHTHALIC ACID PARTICLES IN LIQUID SOLUTION

ABSTRACT

Because of considerable experimental difficulties, the data on 4-carboxybenzaldehyde incorporation in the terephthalic acid crystal does not allow to determine the effects of the major parameters, such as the crystal growth rate, on the separation effectiveness, in this work, a theoretical analysis was done of co-crystallization of two iso-morphous organic substances (terephthalic acid and 4-earboxybenzaldehyde) based on the Monte Carlo simulation of crystal growth. In order to account for the limited solute diffusion velocity thru the boundary layer, analytical solution of a simple model of the boundary layer was combined via an iterative process with the Monte Carlo simulation of the interface. The distribution coefficient of the impurity (4-carboxybenzaldehyde) was found to be largely independent of the impurity level in the solution and an increasing function of the crystal growth rate. In order to compare the theoretical results of this work with experiment, it was suggested to carry out future experiments on entrainment of 4-carboxybenzaldehyde in the terephthalic acid crystal in aqueous dimethyl-sulfoxide solutions at room temperature. Such a system is believed to simulate well the behavior of aqueous terephthalic acid solutions at temperatures around 200°C where the experiments become prohibitive.     

圆饼电离室空气比释动能物理参量的蒙特卡洛模拟

为建立基于圆饼电离室系统的~(60)Coγ射线空气比释动能基准装置,对辐射场及场中电离室的相关物理参量进行了蒙特卡洛模拟研究。通过BEAMnrc程序建立辐照器模型计算测量点处能谱和注量分布,使用EGSnrc计算圆饼电离室在辐射场中各物理参量。~(60)Coγ射线空气比释动能绝对测量装置通过蒙特卡洛模拟得到的相关物理参数合成不确定度为0.20%,该结果与澳大利亚计量院同结构电离室的结果在不确定度范围内一致,与国家基准球-圆柱形电离室及球形电离室相比在不确定范围内符合。     

Comparison of simplified Monte Carlo simulation and diffusion approximation for the fluorescence signal from phantoms with typical mouse tissue optical properties

A simplified approach is proposed to simulate the fluorescence signal from a fluorophore submerged inside a turbid medium using the Monte Carlo method. Based on the reversibility of photon propagation, the fluorescence signal can be obtained from a single Monte Carlo simulation of the excitation light. This is computationally less expensive and also allows for the direct use of well-validated nonfluorescence photon migration Monte Carlo codes. Fluorescence signals from a mouse tissuelike phantom were computed using both the simplified Monte Carlo simulation and the diffusion approximation. The relative difference of signal intensity was found to be at most 30% for a fluorophore placed in the medium at various depths and horizontally midway between a source-detector pair separated by 3 mm. The difference in time characteristics of the signal is also examined.     

基于MATLAB的MCM对GUM不确定度框架验证

测量不确定度评定领域中主要采用的方法是GUM,我国于2012年12月发布了新版JJF1059.1-2012《测量不确定度评定与表示》,并于2013年6月3日起实施。规范提出当JJF1059.1-2012不适用时,可考虑采用JJF1059.2-2012《用蒙特卡洛法评定测量不确定度》进行不确定度评定。同时规范强调GUM的评定结果可以用蒙特卡洛法（MCM）进行验证,验证评定结果一致时仍然可采用GUM进行不确定度评定。文中利用MATLAB数学工具,以实例的方式说明MCM对GUM不确定度框架如何验证并得出相关结论。     

Uncertainty of the Calibration of Paired Temperature Sensors for Heat Meters

In heat meters, the temperatures of the incoming and the outgoing water are measured with calibrated platinum resistance thermometers. They are subject to legal metrology and the requirements for the uncertainty associated with the temperature difference are specified in national and regional standards. It is difficult to calculate this uncertainty, since it depends on the characteristics of both sensors and correlation needs to be considered. Causes of that correlation include calibration in the same facility, losses due to heat conduction, and common electrical measurements. Therefore, an analytical calculation of the temperature difference and the associated uncertainty is quite complicated, requiring several steps, corrections, and approximations. Monte Carlo techniques avoid these difficulties by simulating the calibration of both sensors simultaneously. As expected, the correlation reduces the uncertainty associated with the temperature difference indicated by the sensor pair considerably. Monte Carlo simulation and analytical calculations are briefly described and their results are compared.     

Uncertainty analysis of the urinary excretion of plutonium

A quantitative estimate of the uncertainty of the urinary excretion of plutonium predicted by available biokinetic models is provided. Urinary excretion is primarily considered here because the monitoring of internal contamination of plutonium mainly relies on measurements of activity in urine samples. A previous paper has identified the most significant transfer rates for urinary plutonium excretion following an acute intake. That analysis is used here as a screening method to reduce the number of model parameters to be considered. A log-normal distribution was assumed for the probability distribution of the model parameters. The spread of the values, represented by the geometric standard deviation (GSD), is explicitly calculated, as few indications of the range of variation of systemic transfer rates are available. Different values for the GSD were considered. Assuming a certain GSD for all the systemic rate constants, random values of the rates were generated (by means of a Monte Carlo simulation with a Latin hypercube sampling scheme) and the resulting predictions of urine bioassay measurements were calculated. The comparison of the mean and variance of the predictions with the available data from several studies performed on different subjects provides information about the GSD of model parameters that represents the intersubject variation of transfer parameters.     

Particle Detachment from Rough Surfaces in Turbulent Flows: An Analytical Expression for Resuspension Fraction

The critical shear velocity for resuspension of micrometer size particles from rough surfaces was studied. The random variation of surface roughness was accounted for. The recently developed Monte Carlo simulations accounted for the statistical variations of physical parameters that control the particle resuspension process. A sensitivity analysis showed that the surface roughness and its random variation was the key factor affecting the particle resuspension from rough surfaces. The theory of probabilistic transformation was used and an analytical expression for evaluating the resuspension fraction of particles of different sizes from rough surfaces versus the shear velocity was developed. The resuspension fractions as predicted by the analytical model were evaluated for several particles sizes for a range of turbulent flow shear velocities. The resulting resuspension fractions were compared with those obtained from the Monte Carlo simulations as well as the available experimental data. It was found that the predictions of the new analytical equation were in good agreement with the Monte Carlo simulation results and the experimental data, especially for smaller size particles. This new analytical expression could be used as a simple empirical equation for estimating flow-induced resuspension of particles from rough surfaces.     

Validation by Monte Carlo sampling of experimental observation functionals

We present and analyze a validation procedure for a given state estimate u ^? of the true field u ^true based on Monte Carlo sampling of experimental observation functionals. Our method provides, given a set of N possibly noisy local experimental observation functionals over the spatial domain Ω, confidence intervals for the L ²(Ω) error in state and the error in L ²(Ω) outputs. For L ²(Ω) outputs, our approach also provides a confidence interval for the output itself, which can be used to improve the initial output estimate based on u ^?. Our approach implicitly takes advantage of variance reduction, through the proximity of u ^? to u ^true, to provide tight confidence intervals even for modest values of N . We present results for a synthetic model problem to illustrate the elements of the methodology and confirm the numerical properties suggested by the theory. Finally, we consider an experimental thermal patch configuration to demonstrate the applicability of our approach to real physical systems.     

测量不确定度最大残差系数的一种新算法

在测量不确定度的评定中,用测量数据的最大残差乘以适当的系数获得标准差的方法称为最大残差法。通过对最大残差的分布函数及其数字特征的分析研究,建立了最大残差的概率模型,并且利用蒙特卡罗模拟及Matlab软件,提出了计算测量不确定度最大残差系数的一种新方法,求出了当测量次数小于50时,最大残差所对应的分布函数、均值、标准差和自由度的数值,并给出了最大残差法的系数表。最后通过测量实例验证了理论分析的正确性。用文中提出的方法可简单、迅速、可靠地计算出所需要的标准差数值。